You are performing an electro$-$osmosis experiment to characterize a porous plug of

material $15cm$ long. The conducting solution is an aqueous electrolyte $,$

$E_r=78\mathrm{.}5,$ and $k={10}^{-3}{}^{-1}c{m}^{-1}).$

a$)$ Neglecting any pressure drop across the plug, calculate the zeta potential of the

material if the electro$-$osmotic current is $50$A and the fluid flow rate is $2{10}^{-5}\frac{m^3}{s}.$

b$)$ If a pressure drop of $1\mathrm{.}2$atm is required to arrest the fluid flow, estimate the effective

radius of pores in the plug.